In 2010, after hearing that “The Flat Earth Society” (yes, the same one that the great Thomas Dolby belongs to…do look them up, their history is fascinating) was not merely a parody of scientific clubs, but rather a group founded on and continues to preach their sincere belief that the Earth is flat (in spite of Eratosthones having successfully calculated its circumference 2,200 years ago and…well…pictures and whatnot) and that the “spheroid theory” is a conspiracy propagated by airlines to jack up fares, I found not only their website, but the email address of their president: Daniel Shenton…

(please note that as I am part of the spheroidist conspiracy, I changed my name to my web handle so that I can continue to spread such lies with impunity)

I have come to your website www.theflatearthsociety.org independently (without referrals or prior knowledge of it) and as such I cannot immediately tell, even from the FAQ, what is it’s true purpose. Everything I see there says that it is sincere, but it could be so deeply tongue-in-cheek that I just can’t see the “tell”. Can you please confirm for me in no uncertain terms if the purpose of the society is to…

1 – Forward, promote and discuss a sincere hypothesis that the Earth is flat on the basis that it is a Scientific Theory.

2 – Table an alternate hypothesis to the Round Earth Theory for the purpose attempting to falsify it, thereby improving it (RET). From the forum posts, I can see that it has worked brilliantly for this.

3 – A long-running joke, in that the Earth is just as flat as Stephen Colbert is a Republican.

4 – Some other purpose I hadn’t considered

If it is indeed Option 1 (sincere), it seems less “tongue-in-cheek” than it is “foot-up-ass”. If otherwise, then I applaud you and swill join up ASAP.

While I cannot speak about other peoples’ motives with absolute certainty, I do know that my own falls well within ‘1’ on your list. There are some people on the forums who probably follow ‘2’ or ‘3’, but the Society itself does exist (and always has existed) in order to investigate and promote Flat Earth Theory.

Thank you for writing back to me so quickly and clearly. I see that you are indeed sincere about your acceptance of Flat Earth Theory and that you also appreciate that not everyone who engages with the Society shares your world view. I do have some questions for you, but first one small matter that you may want to clear up with your fellow proponents…

I see on the website a number of references to “Round Earth Theory”. This is misleading in that…

1 – The scientific and popular consensus is not that the Earth is “round” but that it is “spherical” (if maybe bulging a bit along the equator).

2 – Flat Earth Theory (or at least your model of it) suggests that the Earth is a flat, circular disc bordered by a 150-foot tall ring of ice (what we call “Antarctic”). “Round” describes a circular flat object, like a wheel or the Earth as you describe it. As such, the term “round” describes your relatively two-dimensional model much better than it does the more universally accepted one, which is described by the more three-dimensional “sphere”.

…as such, I recommend that you encourage your fellow proponents to refer to the generally accepted model as “Spheroid Earth Theory” and perhaps you might capitalize on this confusion by referring to your fellows as “Round Earthers” when you want to get your foot in the door at otherwise elitist conferences.

Can you please answer some basic questions about Flat Earth Theory…

1 – Can you please explain why it is that you accept Flat Earth Theory over Spherical Earth Theory when the evidence for the latter (which many accept as empirical) appears to so far outweigh the evidence for the former (which many consider outdated)? The only thing that appears to “correct” this imbalance would be massive conspiracy. Is this the case or are there other factors?

2 – Scientific knowledge moves forward as faulty hypotheses are falsified and correct hypotheses survive falsification. In other words, one gets to the stature by trimming away the “non-statue” bits, leaving the statue bits undamaged. We consider Evolution to be “true” because all attempts by proponents and opponents alike have failed to falsify it or the deluge of evidence for it. From what I have read, the opponents of Flat Earth Theory have (in your opinion) failed to falsify or propose any executable experiment that could falsify Flat Earth Theory or the evidence for it. As a proponent of Flat Earth Theory, can you propose an executable (not too expensive, avoids the conspiracy angle and can be done using existing tools) means by which your theory could be falsified? For example, when asked what would disprove the fossil records of evolution, paleontologist JBS Haldane once said, “fossil rabbits in the Precambrian”.

Thanks,

The Kazoo Sutra – Doha, Qatar

Unfortunately, in the 2 years since, Mr. Shenton never replied to my questions. I can appreciate this because I must admit that although my initial email was written with the purpose of giving him as many possible options to chose from, I did already know what his position was and that must have come across as insincere. For that, I apologize…but I did give him some constructive advice in exchange (I’m quite proud of the “Round Earthers” PR bit). Perhaps he has a Google Alert set to bring this post to his attention and we might continue this conversation via this blog?

In the meantime, here is some of the “evidence” that the Earth is flat. If it’s not convincing or doesn’t make any sense, don’t hurt yourself trying to think about it:

The United Nations unintentionally reveal the truth by way of their flag, which shows the Earth as a disc with the North Pole at the center

The Nile only falls a few feet across it’s entire run

Mariners don’t use globes for navigation

Antarctica is uninhabited…because it doesn’t exist. The UN-flag model of the Earth shows that the coast of Antarctica at actually a wall of ice that runs around the edge of the disc

The proponents of Flat Earth Theory either won’t look at or won’t believe contrary evidence, therefore their theory remains unchallenged.

Any evidence that contradicts the Flat Earth Theory is proof of a corporate & government conspiracy against the theory (a boiler-plate conspiracy-theorist rationalization that applies to all such nonsense)

Comments are welcome and encouraged. However, before you post, please read my Moderation Policy, which I’ve adopted to control Spam. Basically, if you link to another website AND you do NOT refer to some specific detail about my post or another commenter’s post, your comment will be trashed before it appears, even if you are kind enough to say only, “I like your blog”. Sorry ’bout that, but the spam-bots have wrecked it for all of us.

The point: Most logical fallacies are merely heurisms – aka educated guesses - taken to unreasonable extremes: causing one to jump foolishly from consideration to conclusion, leading to either delusion or deceit.

The rant that goes with it:

If possession is 9/10ths of the law, then heuristics are the basis of 9/10ths of logical fallacies. Wikipedia describes “Heuristic” as:

…experience-based techniques for problem solving, learning, and discovery. Where an exhaustive search is impractical, heuristic methods are used to speed up the process of finding a satisfactory solution. Examples of this method include using a “rule of thumb”, an educated guess, an intuitive judgment, or common sense.

The saying, “Where there’s smoke, there’s fire” is a good example of a heuristic. For the sake of this post, it is a particularily good example because it is often associated with jumping to conclusions – ie: when gossip is involved.

Heuristics are good for spotting red flags or making safe bets, but they becomes fallacious when they are used to jump to definite conclusions. For example, “He is right because he is the boss” is a classic Appeal To Authority logical fallacy because – even though the chances are probably pretty good that being experienced, qualified and talented enough to become the boss – it is a safe bet that he will probably be right, does NOT mean that he IS right for sure. If this were true, then you would not be justified in questioning his decision if he were to instruct you, say instruct you to carry out the Final Solution…and we all know how THAT worked out for the employees who were put on trial at Nuremberg.

A more straightforward example is this: Someone offers to make a bet over a dice roll. He says he will roll the dice once, take bets and if the second roll matches the first, he will double the betters’ money. He rolls a 6 and calls for bets. The heuristic thinker thinks this is too good to be true (probably a scam using a weighted die that always rolls 6) but he bets $10 anyway because there is an 83% chance he will win if the game is honest and he can afford to lose $10 if he is unlucky or the game is rigged. The fallacious thinker considers the same risks but refuses to bet because he KNOWS it MUST be a scam. The dice rolls up 3. The heuristic thinker takes the $20, wishing he’d bet more but thankful it wasn’t a scam and appreciating the extra $10. The fallacious thinker, upset that he should have gambled his house, resolves his cognitive dissonance by concluding that both of the others were in collusion to convince him to play in a second round with a rigged dice…and runs them over with his car.

Heuristics – as well as the majority of the most common logical fallacies – are intuition based (and in the case of logical fallacies, mixed in with a little bit of confirmation bias and the instinct to grab at straws when losing an argument) thought processes. There is nothing wrong with this so long as we do not delude ourselves into thinking that we the conclusion = knowledge. We have evolved to think in this “chances are…” way because in a pinch, we could make statistical assessments in situations where we didn’t actually have enough facts to be 100% certain. This gives us the power of heuristic thinking, so that we can act in the most reasonable way even without enough facts to know for sure what to do.

However, this power can overwhelm us and we can easily mistake our reasonably-induced statistical assessment for deduction of straight fact. This is where the fallacious logic comes in. This overdriven logical quirk of ours remains in the gene pool because sometimes the situation is SO dire, that we could not make the best choice unless we BELIEVED our conclusion was 100% correct. For example, imagine your great-great-great…great-great grandfather is being chased by a sabre-toothed tiger out of your familiar hunting ground and you came to a fork in the path. To the right, you hear a river and to the left, you hear more tigers growling. He could stand there like a neurotic idiot deliberating whether or not a pride of ventriloquist tigers is waiting by the river while they cast their growls to the left of him (POSSIBLE but highly IMPROBABLE)or he could turn right KNOWING (falsely or not) that the tiger will not follow him into the river. His delusion of certainty allowed him to react unconsciously…and voila, you are here today to be thankful for his assumption.

That being said, your best friend Billy’s great-great-great…great-great grandfather might have made a similar decision in a different forest, except he was extremely unlucky enough to encounter a pride of ventriloquist tigers waiting by the river…as the tiger that was chasing him died of a heart-attack anyway. But of course you don’t have a best friend Billy because he inherited the whole not-existing thing.

The basis of this post is to demonstrate that most logical fallacies are the result of unintentionally mistaking (delusion) or intentionally twisting statistically-reasonable thought processes (deceit) into undeservedly-definite outputs. See how these very common logical fallacies, including the aforementioned Appeal to Authority, fit this description:

The doctor is being sued for malpractice right now, so his diagnosis of cancer must be wrong.

A doctor being under the microscope for medical wrongdoing is an excellent reason to be suspicious of his competence, so best to be cautious and get a second opinion…as long as you have time. However, because the suit could be frivolous or perhaps not related to the subject at hand, you could deprive yourself of a timely warning if you reject his diagnosis outright over the matter of malpractice alone.

I’ve seen the positive test results, I don’t smoke and I refuse to believe that non-smokers can get lung cancer, so the diagnosis is definitely wrong.

Considering that you don’t engage in the most common cause of the diagnosed illness, it could be more likely that the test is a false positive than that you are in the small percentage of people who get such cancer without smoking, but there is still enough chance that you do have cancer to have the tests repeated a couple of times to make sure.

Every time I get close to a doctor, the cancer test comes back positive. Therefore, the doctors’ lab coats must be the cause of my cancer and so I will stop seeing the doctors and wait for the cancer to disappear.

Well…that’s just silly and I won’t try to defend that one. Clearly the real problem is with the doctor’s cancer-infested stethoscopes!

Why all the cancer references? Cancer is an apt metaphor for the runaway effect by which perfectly healthy induction methods breed into destructive and delusional psuedo-deduction methods that compete with and eventually overwhelm the thinker’s faculties for reason, resulting in a complete takeover of the process and eventual death of the good idea.

Although heuristics are a smart and quick way to put your thoughts and focus in (probably) the right direction, they won’t take you all the way to a reliable conclusion. True, heuristics may result in your being right some or maybe even most of the time (if you are extremely lucky), but if you keep up this practice there is a good chance that you will be grievously wrong when it really counts…and when you do fail, prey to the FSM that a logician isn’t standing next to you with his list of logical fallacies, saying “I told you so!” as he cites your specific error.

Comments are welcome and encouraged. However, before you post, please read my Moderation Policy, which I’ve adopted to control Spam. Basically, if you link to another website AND you do NOT refer to some specific detail about my post or another commenter’s post, your comment will be trashed before it appears, even if you are kind enough to say only, “I like your blog”. Sorry ’bout that, but the spam-bots have wrecked it for all of us.

Note: The title of this post is a bit ironic (reason made clear below), but I couldn’t resist it.

The point: Contrary to the commonly misunderstood phrase, rules are not “proven” by having exceptions. Neither do they have to have exceptions in order to be valid. Rather, some exceptions do infer the rule to which the exception is made.

The rant that goes with it:

The phrase “the exception that proves the rule” is often misused to somehow imply that a rule (whether it be a natural law or an abstract one established by people), is somehow validated by having an exception. Not only is this an invalid interpretation of the phrase; it is absurd. If anything, exceptions are more likely to undermine rules than to clarify or bolster them. In science, exceptions tend to lead to the breakdown of theories, resulting in new ones that have fewer or even no exceptions. In the laws of men, exceptions tend to muddy the rules, opening them to abuse, as Napoleon so famously allowed for when he added exceptions to the unambiguous rules that Snowball originally established in George Orwell’s “Animal Farm”:

No animal shall kill any other animal…without cause

Clearly the original rule, sans “…without cause”, was perfectly valid as-was and much more easily interpreted before Napoleon got his hooves on it.

Of course, this rule at “Animal Farm” is merely a reference to the supposedly definitive 6th (or 5th, depending on which “infallible” version you read) Commandment:

Thou shalt not kill

However, in this case, the word “kill” is actually a mistranslation: The original Hebrew text uses the word “murder”, which is an entirely different concept because “murder” allows for “justified killing” that is NOT considered murder, such as when the “priestly legislation” excuses it in warfare (1 Kings 2:5–6), capital punishment for even the most humble of “crimes”, such as cursing one’s parents (Leviticus 20:9–16) and defense of not only oneself but one’s property (Exodus 22:2). The New Testament also describes “murder” as being immoral and agreeing with the exceptions noted in the Old Testament, so the devout can’t simply cherry-pick a version that is benign on the issue. As such, the more accurate way to represent the intent of this Commandment, in English, would be…

Thou shalt not kill…except in warfare, capital punishment, self-defense or any other occasion where you don’t feel guilty* about it.

Although these “exceptions to the (6th) rule” resolve this particular inconsistency in the bible (but there are plenty of others left), they have compromised the clarity of the concept that you shouldn’t kill ANYONE, leaving the door of interpretation wide open for people like Osama Bin Laden and George Bush to “not murder” (with impunity from their own people) those who do not agree with their personal world views. In fact, Moses himself was the first to take advantage of these exceptions when heordered the “killing” (Exodus 32:25–29). of the 3,000 people in his flock who didn’t share histhe FSM’s vision of the future.

One excellent example of an abstract (man-made) rule that has no exceptions is the law absolutely forbidding motor vehicles from the streets of Venice, Italy. No cars are found: not the mayor’s, not for police, no ambulances – none. In fact, this uncompromised rule has been so successfully enforced that the infrastructure of tight pedestrian-only walkways between open spaces and lack of any ground-vehicle fueling stations has caused this to become an almost “natural law”, requiring almost no actual enforcement in order to ensure full compliance.

Contrast this to Rome’s Christmastime vehicle-control laws, established to reduce the amount of traffic on the roads during this busy period. Cars with odd-numbered plates may enter the streets on odd-numbered days and there are exceptions for police, ambulances, “designated” officials, etc. The number of vague exceptions supplemental to this rule make it extremely difficult to enforce, let alone impossible to ensure full compliance. Therefore, these exceptions completely UNDERMINE the rule.

Further to this, I recently had a conversation with someone, to remain nameless (dear), who not only accepted this common interpretation but drew from it the conclusion every rule MUST have an exception. This, too is absurd. Certainly rules CAN have exceptions, but that does not make them requisite. For example, if I tell my son that he cannot have a cookie before dinner, it doesn’t matter how often he asks or how many excuses/scenarios he concocts…he ain’t getting’ one. Likewise, per the second law of thermodynamics, perpetual motion machines shall not be. No exceptions.

So, what IS meant by “the exception that proves* the rule” anyway? The pithy answer:

Sometimes we can infer a rule from its exception, even when the rule is not explicitly stated.

*The term “prove” in the phrase is unfortunate in that proof of the rule is not the issue. The relevant exception doesn’t actually prove anything about the rule…as though the rule had somehow passed some sort of falsification attempt at the hands of the exception. Rather, it merely infersthe existence of the rule. Accordingly, the phrase should have been “the exception that infers the rule”. Yet another flawed meme…

For deeper insight, I invoke an email that I sent this morning to our Health and Safety Manager, in which I ask him how we are meant to interpret the meaning of a controlled right turn at one corner of a jobsite where most of the other intersections have no such controls:

Dear ES&H Mgr:

My comment this morning (that controlled right turns at a few intersections inferring that it is okay to turn right where such controls are absent) is based in the often-misunderstood concept of “the exception that proves the rule”, a description and example of which can be found at the Wikipedia entry on the subject:

The original meaning of this idiom is that the presence of an exception applying to a specific case establishes that a general rule existed. Example (Fowler): “Special leave is given for men to be out of barracks tonight till 11.00 p.m.; “The exception proves the rule” means that this special leave implies a rule requiring men, except when an exception is made, to be in earlier. The value of this in interpreting statutes is plain.”

My favorite simpler example is that when the sign on a door of a shop says “Closed Sundays”, the reasonable implication is that it is open 6 days per week.

Note that in spite of the point that I am trying to make, in terms of formal (deductive) logic one cannot assume that the store is open 6 days because the sign can be true even if the store is also closed on Saturday (not to mention Xmas and New Years) however in the courts, judges appreciate that the IMPLICIT meaning outweighs the EXPLICIT meaning and “The Exception That Proves the Rule” found it’s place in Common Law as “exceptio probat regulam in casibus non exceptis”

As such, by this informal (inductive) logic the inference of the controlled right turn at some intersections is that on this project one is permitted to turn right on a standard red light (perfectly legal in many OTHER countries, including Canada) where no right indicator exists. You confirmed this morning that this is NOT the case in Qatar or on the jobsite, so I strongly recommend removal of the right turn control lights in order to eliminate this confusion.

The only justification for the right-turn controls would be IF the right-turn control lights are not always the same colour as their standard counterparts, making them exceptional. However, there should be a sign on the post saying that is the case. Otherwise, they are not only redundant but also unsafe in that they will cause drivers to inadvertently break the rules at other intersections. And when two people come to an intersection with DIFFERENT interpretations of the rules…

Regards,

The Kazoo Sutra, BArch

Comments are welcome and encouraged. However, before you post, please read my Moderation Policy, which I’ve adopted to control Spam. Basically, if you link to another website AND you do NOT refer to some specific detail about my post or another commenter’s post, your comment will be trashed before it appears, even if you are kind enough to say only, “I like your blog”. Sorry ’bout that, but the spam-bots have wrecked it for all of us.

The point: Change the option of the “Monty Hall Problem” from “switch one door for another” to “switch TWO doors for one door” in order to eliminate the “preference bias noise” of the original version of the problem and make the correct solution even more counter-intuitive.

The rant that goes with it:

In Parts 1 & 2 of this 3-part series, I demonstrated how “Monty Hall Problem” can be intuitively explained, the implication that it has on the reliability of intuition and how such faith in one’s false convictions can expose you to predators…like me. In this Part 3, I propose an alternative version of the problem that I cheekily call the “Jason Hall Problem” (there are those, including my wife, who will tell you that this is merely one in a long list…).

In the “Monty Hall Problem”, the premise of trading one door for one other door often confuses people into thinking the problem is about preference as opposed to statistics. In other words, “If it doesn’t matter whether I stay or switch, staying is better because I stick to my commitments”. Even though these people believe that statistically it doesn’t make a difference, when asked what is the best thing to do they insist that it is either “better” to keep their original choice (if they tilt towards the psychotic) or to switch doors (if they tilt towards the neurotic). The commitment to one or the other over principal alone is very strong, a fact made clear in this anecdote:

While doing the 10-card demonstration (ref Part 2, the trials with my boss) for one of my colleagues, he insisted repeatedly that it was in his best interest to stay with his original choice, even as I continued to explain to him that the actual statistics gave him a 90% chance of winning if he switched. Then I switched tactics: I put $5 on the table and told him that the money was his if he ended up with the winning card. At that point, he said it was obvious that he should switch, which he did. I then asked him, before telling him that he had won the $5, “and if there were no money involved?” His response, amazingly, was, “then I wouldn’t switch”. I concluded from this experiment that some people are really, really messed up beyond saving…and that preference bias is strong, even can be bought-off.

Changing the problem so that the correct answer is to trade away one number of doors in exchange for a different number of doors eliminates this “preference noise” of the original problem. Furthermore, to emphasize counter-intuitive properties of this problem in the revised version, the correct answer must (of course) be one where the player must give away more doors than he gets back in order to have the best statistical advantage. As impossible as this seems, if you truly understand the original version of the problem, it is not so difficult to achieve, as I will explain.

In my version, there are 5 doors rather than 3.

Mr. Hall (that would me ME this time around) asks the contestant to select any 2 doors from the 5…

…and then he (I) open 2 of the unselected doors with booby-prizes (hee hee, that’s funny again). All other parameters of the problem are the same as the original “Monty” 3-door version.

At this point in the 5-door version, the contestant has selected closed doors #1 & #2, the host (that’s me again) has opened doors #4 & #5 to reveal crap prizes and the unclaimed #3 door remains closed.

The question is this: Will the contestant keep BOTH of the doors he picked OR will he trade BOTH of his doors for the ONE closed door that he did not pick? What would YOU do? (please just PRETEND that you don’t know that the problem is engineered so that the least-intuitive answer is the correct one!).

The answer: It is in your best interest to switch (of course)

Although the intuitive response of someone unfamiliar with the statistics involved would most likely choose to keep his two doors on the basis that he apparantly has a 2/3 chance of winning, the corrrect answer is to switch his two doors for the one unselected door because in fact he would be trading a 2/5 chance for a slightly better 3/5 chance of winning, as shown in this “replay” where each guitar pick represents a 1/5 chance of the door hiding the prize:

In the “Jason” case, the chances of winning don’t double like they do in the “Monty” case (making it harder to demonstrate as clearly through trials), but the advantage of switching still exists, because:

One in the bush is worth (more than) two in the hand!

Comments are welcome and encouraged. However, before you post, please read my Moderation Policy, which I’ve adopted to control Spam. Basically, if you link to another website AND you do NOT refer to some specific detail about my post or another commenter’s post, your comment will be trashed before it appears, even if you are kind enough to say only, “I like your blog”. Sorry ’bout that, but the spam-bots have wrecked it for all of us.

The point: When it comes to matters-of-fact, logic/evidence-based positions are superior to intuition-based positions and this can be exploited for profit.

The rant that goes with it:

In Part 1 of this 3-part series, we saw how learning to intuitively appreciate the “Monty Hall Problem” demonstrates that intuition alone is not a reliable means of determining the way things actually work. In this part, I anecdotally will show how this knowledge can be used to really screw people over. Remember: with such great power comes great responsibility, not to mention the chance of getting your teeth smashed-in, so wield this weapon with respect and care!

The beauty of the “Monty Hall Problem” is that although it is just as easy to come to the wrong conclusion as it is difficult to accept the correct conclusion, the right answer can be proven, in court if necessary, making it a perfect tool for a con artist. The idea is simple: If the wrong answer is so intuitive that someone will remain committed to that wrong answer, even AFTER you’ve TOLD them the correct answer, the opportunity to convince them to place a high-stakes wager against the answer that you can ultimately PROVE to be correct is very difficult to resist to any self-respecting swindler. It is the timeless story of using someone’s greed against them. Case and point:

In 2009 while I was working under an expat contract in Qatar, I aspired to attend The 7th Amazing Meeting (TAM7)conference on critical-thinking in Las Vegas with my son Adrian. Unfortunately, I was unable to go because the project was at a critical stage and the Area Manager refused to grant any leave during that period. This was doubly-unfortunate because I had chosen to split my one annual business-class ticket entitlement into two economies, one of which I had already used to go to Canada (for far less than the value of ½ a business-class) and the right to use balance towards the value of second ticket was about to expire. In short, I wanted to go ½-way around the world to Las Vegas and if only the ADM would sign-off, I would get there and back for free.

Like a kid repeatedly asking his dad for a cookie before dinner, I asked him three times to authorize the trip and like the prick that my dad could be, he continually refused to provide a cookie…er…his signature. Finally, he asked me, “What’s this conference all about anyway?” I told him, “it’s about skepticism and critical thinking”, to which he replied, “what’s critical thinking?”

I explained to him that critical thinking is all about the application of high standards of introspective analysis when forming or considering ideas and that this includes the very challenging tasks of filtering out personal bias, recognizing fallacious logic, questioning dubious premises, learning to accept evidence-based conclusions even if they are inconvenient to you, etc. Considering his perplexed look, I decided to give him an example. I described the “Monty Hall Problem” to him and told him that the techniques of critical thinking help to cut through the intellectual noise that prevent one from not only coming to, but appreciating the correct solution.

When I gave him the question of whether to switch, stay or tell me it doesn’t matter, he came to the intuitive-based conclusion “it doesn’t matter whether I stay or switch” and then scoffed at the correct answer of “best to switch” when I gave it to him. Both of these are common responses, however, even as I explained the logic behind the reason for switching doors, he continued to stand by his original conclusion, becoming very distressed in the process. He apparently had trouble dealing with someone so deluded by such pseudo-math and misguided thinking.

Seeing an opportunity, I proposed, “If you are so sure that I’m wrong about this, then ‘Let’s Make a Deal’, shall we? If I can get you to admit that your answer is wrong and mine is right in less than 10 minutes, you sign-off on our trip to Las Vegas. If I can’t do this in 10 minutes then I will stop asking for your signature and you’ll never hear of this again.”

“You’re on!” he exclaimed, certain that he couldn’t possibly lose.

In the first 2 minutes, I explained the 10-ticket Scratch-&-Win analogy to him, but he wasn’t impressed (I said that it was a good teaching device; I never said it worked EVERY time).

Having failed at the theoretical, I went for the practical in the form of repeated trials: I dug through my desk (typically a pig-sty, iso that cost me another 2 minutes) and found a deck of cards. I took out 9 red-suit cards and one black-suit card to represent losing and winning tickets respectively, shuffled them and put the 10 cards face-down in a row front of him such that I knew where the black suit was. I had him select a card and then I turned up 8 red cards, leaving his card and the 10th face down on the table. I then asked him, “stay or switch?” True to his belief, he said, “It doesn’t matter”. When he turned over his card, it was a loser. Of course, we know there was a 90% chance that it lose, no surprise there.

We repeated the exercise 10 times over the next three minutes (for those of you who have lost track of time, we are now 7 minutes towards the 10-minute deadline). I recall that through all these trials, he held the winning card only twice, which although one better than chance according to theory, was enough for him to eventually look up in shock as though he had just realized that he left a baby at the grocery store, then face-palm and utter through his sweaty fingers, “oh, f**k me!”

Yes, he got it eventually, and fully 2 minutes before my time was up. He signed and I sent him a postcard from Las Vegas. TAM was awesome, by the way.

I have since been tempted to run this sure bet for cash, but I just can’t bring myself to do it because I have a terrible poker-face and I just can’t bring myself to take advantage of people in such a way (…very often). Perhaps you are not so principled as I am. Good luck with that.

In the final Part 3 of this series, I propose an alternate version of the problem that both eliminated the 50/50 conundrum with the added benifit of being more counter-intuitive than the original.

Comments are welcome and encouraged. However, before you post, please read my Moderation Policy, which I’ve adopted to control Spam. Basically, if you link to another website AND you do NOT refer to some specific detail about my post or another commenter’s post, your comment will be trashed before it appears, even if you are kind enough to say only, “I like your blog”. Sorry ’bout that, but the spam-bots have wrecked it for all of us.

The point 1: “The Monty Hall Problem” demonstrates that one cannot rely on intuition alone to determine the “truth” of a matter and as such, this should cause one to question their faith in intuition-based ideas.

The point 2: The correct but counter-intuitive answer to “The Monty Hall Problem” (I don’t want to give it away here) is made intuitive via a Scratch-&-Win lottery ticket analogy.

The rant that goes with it:

For those of you who don’t know what what is meant by “The Monty Hall Problem”, I will explain shortly. First, a short pre-amble on intuitive thinking…

There are those who believe that their instincts provide better insight into the workings of the universe than hard evidence and sound logic, even when the evidence and (often biassed) instincts are in conflict. For example, renowned anti-vaccination advocate and child-killer-by-proxy Jenny McCarthy, who almost single-handedly brought back such popular diseases like Measles and Mumps solely on the basis that her “mommy instincts” outweigh well-established scientific modalities, is one such person. I developed and occasionally teach a course on Information Management that uses the “Monty Hall Problem” (some call it a “paradox”, but I argue that there are no such things as true paradoxes. That is a subject of another post…) to demonstrate that SOME things which appear to be bone-headedly obvious might not be true at all – no matter how much they seem so. Friedrich Nietzsche summed this concept up beautifully when he said:

A casual stroll through the lunatic asylum shows us that faith proves nothing.

On hearing my enthusiasm for this quotation, one may invoke Voltaire, who said, “A witty saying proves nothing”, which does apply to something like, “The best things in life are free”, because one could easily challenge the meaning of “free” or provide examples of favorite things that are not free.However as witty as Nietzsche’s saying is, it isn’t so shallow as that. He states no premises that require substanciation. Regardless of your beliefs or your feelings towards Mr. Nietzsche, this statement stands on its own in that the logic is valid and we all understand the premises (that most if not all of the lunatics are delusional in spite of their personal convictions, a point logically proven if they disagree with each other) to be true – axiomal, if you will. If you question my statement about the premises, please reply with an explanation why.

I was first impressed with the validity of this sort of logic (and became aware of phenomenological arguments and post-modern thinking…both of which are despicable, but that may be the topic of a future post) when I first saw John Carpenter’s wonderful 1974 sci-fi film “Dark Star“, in which the crew of a spaceship attempts to convince an artificially-intelligent bomb not to explode (click to watch video of this scene); the problem being that the bomb-bay doors have failed to open but due to a communication glitch, the bomb is convinced that it has already been dropped and therefore MUST explode in order to “fulfill its destiny”. To make matters worse, the crew cannot manually stop the countdown…only the sentient bomb has the ability to do this.Unfortunately, no matter how hard the crew tries, they cannot convince the bomb to stop the countdown because they cannot convince the bomb that it hasn’t been dropped: all of it’s (damaged) sensors says that is is on it’s way to its target.

Acting Captain Doolittle decides that the best strategy is to “teach it phenomenology”, whereby they enlighten the bomb to the idea that our perception of the universe is a product not of actual reality, but the information that our senses provide to us…and that information could be wrong, therefore the bomb should question the order to explode. Although phenomenology usually doesn’t get you anywhere, Doolittle capitalized on that aspect when he used it to confuse the bomb into questioning its objective to explode:

DOOLITTLE: How do you know you exist?

BOMB #20: It is intuitively obvious.

DOOLITTLE: Intuition is no proof. What concrete evidence do you have that you exist?

DOOLITTLE: How do you know that the evidence your sensory apparatus reveals to you is correct? What I’m getting at is this: the only experience that is directly available to you is your sensory data. And this data is merely a stream of electrical impulses which stimulate your computing center.

BOMB #20: In other words, all I really know about the outside universe relayed to me through my electrical connections. Why, that would mean…I really don’t know what the outside universe is like at all, for certain.

Once the bomb understands this idea, it asks the obvious question…

BOMB #20: True, but since this is so, I have no proof that you are really telling me all this.

…but Doolittle eloquently explains…

DOOLITTLE: That’s all beside the point. THE CONCEPTS ARE VALID, WHEREVER THEY ORIGINATE!

…and such is the power of internally-consistent logic.

Back to the Nietzsche quotation – his point was basically this: although faith may provide oneself with INTERNAL CERTAINTY (to know…), that does not necessarily translate to EXTERNAL ACCURACY (…but be wrong anyway) as demonstrated by the mutually exclusive, and often disproven, beliefs of the asylum tenants. Or, as Mark Knopfler of Dire Straits sang in “Industrial Disease”:

Two men say they’re Jesus…ONE of them must be wrong!

But I digress; For the purpose of this post, perhaps we should re-word Nietzsche’s statement as…

A casual look at the history of the Monty Hall Problem shows us that intuition proves nothing.

The challenge of opening people’s eyes to the idea that their cherished instincts can be wrong is that unless you actually gain THEIR acceptance of your position, you have failed. It is one thing to show someone up in a debate in front of an audience and convince the fence-sitters that your idea is supported by the evidence, but it is quite another thing to win the hearts and minds of those who are dug-in to their opposing view (ie – the dogmatic opponent). In fact, the advice usually given to scientists that are about to debate pseudo-scientists – those who abide by fallacious logic and manufactured evidence for a living – is that they shouldn’t even bother trying or they will end up being the one in the insane asylum. But for those up to the challenge, this post provides a means of confronting the power of intuition head-on.

What is “The Monty Hall Problem”?

For those who are unaware of the by-now-very-well-known “Monty Hall Problem” or have seen the movie “21”, I will briefly describe it here. Skip the next three paragraphs to tthe asterix* if you know the problem and solution, even if you don’t agree with the consensus opinion…

In the very real 1970s game show, “Let’s Make a Deal”, the host (actually fellow Canadian Monty Hall – no relation) presents to you three closed doors that are non-descript except for their being numbered 1, 2 & 3.

You are both aware that behind one door is a valuable prize and behind the other two are little more than booby-prizes. Yes, actual boobies can be an awesome prize, but in this case it’s just an expression for “prize having no value”. You do not know behind which door is the real prize but everyone, including yourself, is aware that Monty, and only Monty, knows which door conceals the real prize. He asks you to pick a door (which you do – ie, #1).

As AT LEAST ONE of the remaining doors is certain to have a booby-(ha…boobies!)-prize and Monty knows which one it is, he opens a booby-(joke gets tired fast)-prize door (ie, #3) leaving two closed doors: Yours (#1) and the other one (#2).

Monty then gives you the opportunity to change your selection (Note: in the show’s history nobody was ever stupid enough to pick the door that Monty had already opened).

The question is this: Is it statistically advantageous to…
(a) stay with the original choice of door #1
(b) switch to unselected door #2 or
(c) do niether (a) nor (b), because it makes no difference?

The most common answer, based on the intuitive conclusion that if it’s either #1 or #2 then there must be an EQUAL chance of the big prize being behind either door, is “(c) – It makes no difference”.

Less common but in my experience still quite common is response “(a) stay with the original choice”, however this response typically comes from people who confuse “statistically advantageous” with “I commit to my decisions”.

Although wrong, the former (c) group tend to be smart people who, like most of us, are simply unaware of the actual statistics at play here (until recently even Nobel-prize-winning mathematicians got it wrong). However, the latter (a) group tend to be dogmatic-minded magical-thinking dumbf**ks that consider their random guesses to somehow transcend logic and evidence.

By elimination (and by statistical proof) the correct answer is “(b) switch to the unselected door”.

*Before you reply to this post with complaints that I am part of the conspiracy to confuse people with mathematical trickery to “prove” something that cannot be true (ala the dastardly Zeno’s Paradoxes such as “Achilles and the Tortoise”, which do this), I say this:

The simplest explanation: When you start out, each door has a 1/3 chance of being a winner.

When you select a door, the chances yours is a winner is 1/3 and therefore the chances that the prize is behind a door you didn’t select is 2/3.

Everyone knows that AT LEAST ONE of the two unselected doors is a loser, so when Mr. Hall opens it, he does not change the 1/3 chance that the door you selected is a winner. Rather, he has merely let you know which of the two unselected doors would have been a bad choice.

Therefore, the chances that the prize is behind the other unselected door is 2/3 because 1/3+2/3=1, where the “1” represents the 100% chance that the prize is SOMEWHERE behind the 3 doors.

Google the problem and look at other (mathematical, logical, trials) solutions. If you don’t like them, then it sucks to be you – so get with it…this problem has swung from a sizable amount of of the mathematical community having previously being convinced that it doesn’t matter which door you pick back when the problem was first identified over 20 years ago, to presently the vast majority (there are still some fringe holdouts amongst mathematicians, like those very few “scientists” that are also creationists – ref “Project Steve“, but these are handy a litmus-tests for incompetence as far as I’m concerned) of generally the SAME COMPETENT PEOPLE convinced that it is statistically advantageous (66% likelihood of winning) if you switch doors, after both doing the relevant math and through real-world test trials required by the last of the hold-outs.

I, too ONCE swore that the answer was (a) and it wasn’t until I had an epiphany* that I came to not accept but understand, INTUITIVELY, that the correct answer is indeed (b). This was a paradigm-shifting moment for me because at that instant, any unfounded faith I may have had in anything (not that I had much to begin with, mind you) immediately evaporated and I became a “born-again” skeptic.

It simply works: My newfound appreciation of the problem provided me with elevated powers to screw with people (I will get to this later).

*No, that wasn’t her stripper name. The following is the epiphany I mention in my statement #3 above…

Imagine you are at your local convenience store and the proprietor has the only lot of 10 scratch-&-win tickets. Let’s say that he lost his licence to sell State-run lottery tickets and in order to stay in the business he is running his own (fair) lottery.

One of the $10 tickets has a big-money payout ($90, which supposedly guarantees the proprietor a profit of $10, but of course only if he sells them all and continues to do so once someone wins). The remainder are worthless.

As he was the creator of this special lottery, it is no secret that the proprietor already knows which of the tickets is good for the prize.

You randomly select a ticket from the pile and pay him the $10 for it.

The proprietor, who was stupid enough to lose his licence with the State and also stupid enough to think he will make a profit on the game if he (likely) sells the winning ticket before the 90th sale, offers to make the game “a little more interesting”.

He says, “give me $60 and I will increase the chances of your winning the $100 from 10% to 50%. Although the statistics of this is NOT quite in your favour, you were dumb enough to buy a lottery ticket in the first place (or perhaps you are just REALLY curious and want to see where this is going), you accept the challenge and give him $60 for a supposed 50/50 chance to not quite double your money.

Knowing that there are AT LEAST 8 losing tickets left in his pile (9, if you picked the winner) as well as which ticket is the actual winner, he scratches 8 of the unselected tickets, leaving one unscratched ticket in your hand and one in front of him on the table. Both of you know that one of these is the winner.

He says to you, “Now, you can have either the one in your hand OR the one on the table. Which one do you want?” It is now clear that he only and erroneously THOUGHT it was 50/50 odds.

However, you remember that when you started the game, the chances of the ticket you originally chose being the winner was only 10% and therefore deduce that the chances of the winning ticket remaining in the pile was 90%.

When the proprietor scratched those 8 losing tickets, the original conditions never changed: The chances that the winning ticket remaining on the table continues to be 90%: he simply separated the wheat from the chaff and chances are that he has inadvertently told you where to MOST LIKELY find the winning ticket.

You happily swap tickets knowing that there is a 90% chance that your $70 investment returns the $100 prize for a profit of $30.

Now, imagine this same game with only three doors…Oops…tickets.

Go have a drink and a think and then come back to read on…

Throughout the entire run of “Let’s Make a Deal”, nobody understood the actual statistics behind the game. It would have only taken one wary statistician to bring this to light in order for the producers to feel the economic pressure to change the rules. It wasn’t until years after it was cancelled that someone figured it out, and she was the object of extreme and unwarranted (but thankfully, not lasting) professional revulsion for years after that.

This post has become absurdly long, so I am breaking it into three parts. Hopefully you now have greater appreciation for not only the elegance and practicality of the correct answer, but also – if the correct answer was a surprise to you – appreciate the implication this has on intuition-based belief sytems, which include faith.

In Part 2 of this series, I will tell the story about how I used the “Monty Hall Problem” to swindle an over-confident employer into sending me to the TAM7 conference in Las Vagas and in Part 3 I will describe my own version, which I call “The JASON Hall Problem” (I’m not an egomaniac, I just couldn’t resist the name), which is an improvement on the original in that it changes the most common intuitive answer from “stay or switch: it doesn’t matter” to “definitely stay”, whilst the correct answer is still to switch.

Comments are welcome and encouraged. However, before you post, please read my Moderation Policy, which I’ve adopted to control Spam. Basically, if you link to another website AND you do NOT refer to some specific detail about my post or another commenter’s post, your comment will be trashed before it appears, even if you are kind enough to say only, “I like your blog”. Sorry ’bout that, but the spam-bots have wrecked it for all of us.

Kazoogories:

Guitarchives:

Spam-pires Beware:

Due to the plague of spamdexing, any replies that don't acknowledge the content of the post will be TRASHED or marked as SPAM (if the link is commercial), no matter how complimentary the reply may be. I reserve the right to harrass such spammers from my sacrificial yahoo email account.